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marishachu [46]
3 years ago
8

Part 1: Joe and Hope were both asked to factor the following polynomial completely. Is one of them correct? Both of them? Neithe

r of them? Explain what each of them did was correct and/or incorrect.
Part 2:

Find all the values of k so the the quadratic expression factors into two binomials. Explain the process used to find the values.

3x^2 + kx - 8​

Mathematics
2 answers:
Arte-miy333 [17]3 years ago
7 0
<h3>Part 1</h3>

If we simplify, both Joe and Hope factored the polynomial correctly but Joe didn't complete it fully.

<u>The first binomial can be further factored:</u>

  • 8x + 12 = 4(2x + 3)
<h3>Part 2</h3>

The quadratic expression needs to have two roots in order to be factored as two binomials.

<u>The discriminant must be positive or zero:</u>

  • D = b² - 4ac ≥ 0

We have a = 3, b = k, c = -8

<u>So we get following inequality:</u>

  • k² - 4*3*(-8) ≥ 0
  • k² + 96 ≥ 0

<u>Since k² is positive for any value of k, the solution is any value of k:</u>

  • k ∈ R
velikii [3]3 years ago
7 0

Hope this attachment helps you.

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SCORPION-xisa [38]
The area of a rectangle can be calculated by the product of its length and the width. Here we are given the area and the length so we can simply calculate for width. The perimeter is the sum of all the side lengths of the shape. We calculate as follows:

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Hope this answers the question. Have a nice day.
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Look at pic down underrr
dimulka [17.4K]

Answer:

Triangle rsu = Triangle tus

Statements Reasons

UR ≅ TS  Definition of Rectangle

US ≅ US Reflexive Property

<U, <T, <R, <S are all congruent and right angles

Definition of Rectangle

ΔRSU ≅ ΔTUS Side, Angle, Side

UR ≅ TS     CPCTC

Just draw a reverse angle,hence you get comparison.

So, satisfying S-S-S

RUS  ≅ SUT

RSU ≅ TUS

So, angle

URS = angle TUS

2. Pythagoras Theorem

Triangle RUS

A^2 + B^2 = C^2

Uu^2 + Ss^2 = Rr^2

√Rr = Rr^2 = x

Triangle TUS

A^2 + B^2 = C^2

Ss^2 + Uu^2 = Tt^2

√Tt = Tt^2 = x

UR measure / sin (60) x (90) = US measure.

ST measure / sin (60) x (90) = US measure.

Proves angles RSU = 30 degree

Proves angles  TUS = 30 degree

As all adjacent angles in a triangle add up to 180 degree.

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Answer:

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Hope this helps!

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